PSI - Issue 8

Amir Pourheidar et al. / Procedia Structural Integrity 8 (2018) 610–617 A. Pourheidar et al. / Structural Integrity Procedia 00 (2017) 000–000

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Fig. 2. Finite element modeling: (a) global geometry; (b) mesh refinement in the critical location;(c) insrting the crack in the sub-model; (d) refined structural mesh around the crack

of interest. The material was idealized as a linear-elastic steel, having Young’s modulus E = 210 GPa and Poisson’s ratio v 0.3. The implemented model is represented in Fig. 2. Axle and auxiliaries were modeled separately, and joined through a surface to surface coupling, including the interference fit option, for taking into account the stresses from press-fit; the mean value of the interference, and 0.3 as friction coe ffi cient, were adopted. Two separate steps were adopted for the application of the loads: during the first step, only the non-linear contact with interference fit option was applied, then, in the second step, the pure bending in the notch were accomplished by applying a linear pressure on the axle cross-section. The non-linearity e ff ect of press-fit simulation on the longitudinal stress path across the thickness in the crack plane was investigated by applying the press-fit interference and bending moment simultaneously and compared with results first procedure. The results of Fig. 3c demonstrates that, there is no significant di ff erence between the two procedures in terms of stress paths,however,there is a huge di ff erence from the point of view of computation time, in which clearly speaks in favor of, considering the bending loading and press-fit e ff ect separately in the analysis. As it can be seen in Fig. 3a, due to the press-fit, the wheel squeeze the axle under its seat and the surrounding regions stretches, as a consequence, a long with the applied bending stress the probability of developing a crack is increases in the geometrical transition. In particular case, when the geometry transition is severe the press-fit e ff ect become dominant and acts as a mean stress and it is not negligible. Madia et al. [7] presented set of equations based on the Carpinteri [8] solution, already taking into account the rotary bending, by introducing the mean contribution to the SIFs at the deepest and surface points of a crack front. The J-integral was obtained for eight contours at the crack front, it can be seen in Fig. 4 that a stabilized SIF is obtained from the second contour upwards. The path independence of the J-integral is an index of the good quality and reliability of the mesh refinement. To calculate the boundary correction factor f, the SIF was scaled to the maximum nominal stress σ N in the minimal cross section with the diameter d of the uncracked shaft. For the deepest point of the crack front A, the calculated energy release rate can directly used for obtaining the stress intensity factor. however 1 √ r singularity of the stress state is not full-field in general for surface cracks in the near surface domain( point C). Due to this boundary layer e ff ect, the classical SIF is not accurate. In order to calculate SIFs at the surface point a normalized distance of 0.05 was considered. Table 3.1 summarizes the evaluated SIF values and corresponding shape factors for 25 di ff erent crack configura tions, by considering the rotary bending e ff ect and residual stresses induced by press-fit at assessment location.